Testing the hypothesis that solvent exchange limits the rates of calcite growth and dissolution

It is established that the rates of solvent exchange at interfaces correlate with the rates of a number of mineral reactions, including growth, dissolution and ion sorption. To test if solvent exchange is limiting these rates, quasi-elastic neutron scattering (QENS) is used here to benchmark classical molecular dynamics (CMD) simulations of water bound to nanoparticulate calcite. Four distributions of solvent exchanges are found with residence times of 8.9 ps for water bound to calcium sites, 14 ps for that bound to carbonate sites and 16.7 and 85.1 ps for two bound waters in a shared calcium-carbonate conformation. By comparing rates and activation energies, it is found that solvent exchange limits reaction rates neither for growth nor dissolution, likely due to the necessity to form intermediate states during ion sorption. However, solvent exchange forms the ceiling for reaction rates and yields insight into more complex reaction pathways.


Powder X-ray diffraction of calcite nanocrystals
The red straight lines show standard diffraction positions and relative intensities of bulk calcite powder peak.
Method: Sample powders were lightly pressed onto a zero-background quartz plate and were characterized using a PANalytical Empyrean X-ray diffractometer (Cu-Kα radiation) with patterns recorded from 5° to 90° 2θ and counting for 0.185 sec at each 0.026° 2θ step, i.e., 10 min measurements.

4.
Analytical model fit to the QENS data.

Figure S4
. QENS spectra line width analysis for calcite nanoparticles with a few layers of sorbed water, showing fitted results at 265, 255 and 245 K.
In each plot, the eight different values of Q are displayed in a sequence of 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5 and 1.7 Å -1 (front to back).Experimental points are shown as blue circles with error bars smaller than the symbols.Black lines are the best fits based on the global Q-dependent fitting procedure.Similar quality of fits was obtained for the 260, 250 and 240 K data and are not shown here.

Calcite water coverages
Snapshots of CMD simulations of different water coverages on the calcite {104} surface are shown below:

3D density plots
To visually identify the various states of water molecules: bound to either the Ca-site,

Radial distribution functions
To define the threshold of whether a water molecule is bound or unbound to the surface site, the minima of the first and second shells from the radial distribution are used for this cutoff.For the calcium site, if the oxygen on water (O w ) is within 3 Å of the calcite (Ca), it is considered bound.If the hydrogen on water (H w ) is within 2.3 Å of oxygen on the carbonate (O CO3 ), it is considered bound to the carbonate site.There is a third possibility that the water can be bound to a bidentate site (Ca-O w and H w -O CO3 simultaneously) for which both the cutoff criteria are satisfied at the same time.

8.
One vs two Gaussian peaks fit for the CO 3 site and shared Ca-CO 3 site The solvent exchange distribution was fit to one and two gaussian models for a) CO 3 site and b) shared Ca-CO 3 site.Row c) The ratio of the χ 2 values calculated for a singlegaussian fit to a double-gaussian model is compared for all the temperature values.If χ 2 = 1, there is perfect agreement between one and two gaussian fits.It is observed that there isn't a large difference in fitting the CMD-derived solvent distribution to one or two gaussian fits for the CO 3 site (values are relatively close to 1).Whereas the doublegaussian model represents a better fit (~ 3 times better) than the single-gaussian fit for solvent exchange on the shared Ca-CO 3 site, clearly emphasizing the need to use a twogaussian model.

Figure
Figure S4.QENS spectra line width analysis for calcite nanoparticles with a few layers of sorbed water,showing fitted results at 265, 255, and 245 K.Each plot displays the eight different Q values in a sequence of 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, and 1.7 Å -1 (front to back).Experimental points are shown as blue circles with error bars smaller than the symbols.Black lines are the best fits based on the global Q-dependent fitting procedure.Similar quality of fits was obtained for the 260, 250, and 240 K data and are not shown here.

Figure S6 .
Figure S6.Number densities of water as a function of distance from the surface for all water coverages

Figure
Figure S7.Chi-squared (χ 2 ) values of each water coverage as a function of q values over a range of temperatures from 240 to 265 K and for different water coverages, a) 845 waters, b) 1690 waters, and c) 3380 waters.

Figure S8 .
Figure S8.Probability isosurfaces of water oxygens (O w ) on calcite surface.The atoms correspond to calcium (red), carbon and oxygen of carbonate (green and pink, respectively), and the oxygens of water corresponding to 845 water coverage (light blue) and 1690 waters (orange).Figure a), b) and c) are isosurfaces viewed along different planes of the surface.Figure d) is the top view of the water directly associated to the surface.

Figure S9 .
Figure S9.Radial distribution functions (solid line) and coordination numbers (dashed line) of Ca (left-blue) and CO 3(right -green) sites on calcite {104} surface with water.

Figure S10 .Figure S11 .
Figure S10.Residence time distributions of water exchanges occurring at the a) CO 3 site and the b) shared Ca-CO 3 site on the Calcite {104} surface.Each column represents a different surface site with the first row representing the residual of the distribution of water exchanges (red curve, second row) to the log-normal fits (blue curve, second row) and its respective deconvolutions (orange + purple, bottom row).c) distribution of χ2 value over the temperature ranges.The value on the y-axis is the ratio of χ2 value single-gaussian fit to double-gaussian model is compared for the temperature values and site configurations.

Table S1 .
The y-intercept HWHM (in eV) and the slope from the global Q-dependent fit.

Table S2 .
The residence times (in ps) and activation energies (kJ/mol) were determined from the fits.